Optical Taps

Yes, it is possible to steal data from a fiber optic cable.

Fiber optics works by shining light down a very narrow core of pure glass (or plastic for shorter distances). So narrow in fact that the light rays don't have room to bounce around (single-mode fiber), or else bounce around in narrow, controlled ways (multi-mode fiber).

However, if you bend the fibers sharply enough, some of the light will leak out (refract through the wall instead of reflecting off of it), as shown in the video here.

Then you just need a gadget to receive that light and convert it back into electrical information. These are easy to come by, it's what is normally at the far end of the fiber anyway. Seem hard to believe? It shouldn’t be; the NSA even does it with undersea cables. All you need is a submarine;)